A325810 Lexicographically earliest sequence such that a(i) = a(j) => A034460(i) = A034460(j) and A325814(i) = A325814(j) for all i, j.

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 35, 2, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 45, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Offset: 1

Author

Antti Karttunen, May 23 2019

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A034460(n), A325814(n)].

For all i, j:

A324400(i) = A324400(j) => a(i) = a(j),

a(i) = a(j) => A033879(i) = A033879(j),

a(i) = a(j) => A325811(i) = A325811(j) => A325813(i) = A325813(i).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A033879, A034460, A324400, A325811, A325813, A325814.

Programs

PARI

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A034460(n) = (A034448(n) - n);
A048146(n) = (sigma(n)-A034448(n));
A325814(n) = (n-A048146(n));
v325810 = rgs_transform(vector(up_to,n,[A034460(n), A325814(n)]));
A325810(n) = v325810[n];